where \( X_iX_j\)  is a tensor product of Pauli \(X\) -type operators on qubits \(i\)  and \(j\) , and \(\theta \)  is the MS-gate angle.
We focus on this version of the MS gate because the fully-entangling MS gate \(XX_{ij}\left(\pi /2\right)\) , together with single-qubit rotations, are sufficient to enact the CNOT gate (see Fig. REF ), which is the two-qubit gate most often used to describe QEC circuitry [1]}, [2]}.
